American Journal of Physics
We derive the rotational form of Newton's second law tau = I alpha from the translational form (F) over right arrow = m (a) over right arrow by performing a force analysis of a simple body consisting of two discrete masses. Curiously, a truly rigid body model leads to an incorrect statement of the rotational second law. The failure of this model is traced to its violation of the strong form of Newton's third law. This leads us to consider a slightly modified non-rigid model that respects the third law, produces the correct rotational second law, and makes explicit the importance of the product of the tangential force with the radial distance: the torque. (C) 2015 American Association of Physics Teachers.
Daniel Cross. 2015. "The physical origin of torque and of the rotational second law" American Journal of Physics 83 (2):121-125.